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An Introduction to Swaps
A swap is an agreement between counter-parties to exchangecash flows at specified future times according to pre-specifiedconditions.
A swap is equivalent to a coupon-bearing asset plus acoupon-bearing liability. The coupons might be fixed orfloating.
A swap is equivalent to a portfolio, or strip, of forwardcontracts--each with a different maturity date, and each withthe same forward price.
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A Plain Vanilla Interest Rate Swap, I.
Party B agrees to pay a fixed payment andreceive a floating payment, from counter-party
A.
Party B is the fixed rate payer-floating ratereceiver (the pay-fixed party).
Party A is the fixed rate receiver-floating ratepayer (the receive-fixed party).
Typically, there is no initial exchange of principal(i.e., no cash flow at the initiation of the swap).
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Quoting Plain Vanilla Swaps
Typically, the floating index, e.g. LIBOR, is bought or sold flat.
If you buy LIBOR (pay-fixed), you pay a spread over the mostrecently issued Treasury with the same maturity as the swap (theasked swap spread).
If you receive fixed (sell LIBOR) then you receive the Treasuryrate plus the bid swap spread, which is smaller than the askedswap spread.
Example:
For a 5-year swap, a dealer might quote 20 (bid) and 24 (asked).
Suppose the yield midpoint of the most recently issued 5-year T-noteis 5.40%.
Then, the pay-fixed party will pay 5.64%, and receive LIBOR.
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Typical Uses of an
Interest Rate Swap
To convert a liability from:
a fixed rate to floating rate. a floating rate to fixed rate.
To convert an investment (asset) from:
a fixed rate to floating rate.
a floating rate to fixed rate.
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Other Interest Rate Swap Structures Off market swaps: The fixed rate may be away from the
market; an initial payment will have to be negotiated.
Amortizing swap: varying NP according to a predeterminedschedule.
Index amortizing swap: The NP, or term of the swap, variesaccording to some randomly changing interest rate index.
Basis swap: The two interest rates both float (e.g., LIBOR
and the prime rate; or 2-year Treasury rate and 10-yearTreasury rate).
Forward swap: The first cash flow takes place in the farfuture, long after the terms of the swap have been
negotiated.
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Currency Swaps There are four types of basic currency swaps:
fixed for fixed.
fixed for floating.
floating for fixed.
floating for floating.
N.B.: It is the interestrates that are fixed or floating.
Typically, the NP is exchangedat the swapsinitiation and termination dates.
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Typical Uses of aCurrency Swap To convert a liability in one currency into a liability in
another currency.
To convert an investment (asset) in one currency to aninvestment in another currency.
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An Example of a Fixed forFixed Currency Swap
An agreement to pay 1% on a Japanese Yenprincipal of 1,040,000,000 and receive 5% on aUS dollar principal of $10,000,000 every year for 3years.
In a currency swap, un l ike in an interest rate
swap, the pr incipal is exchanged at the
beginning and at the end of the swap.
Note that in currency swaps, the direction of the
cash flows at time zero is the opposite of thedirection of the subsequent cash flows in the swap(see the next slide).
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Cash Flows in a Fixed-for-Fixed Currency Swap
At origination:
Party A Party B$10,000,000
1,040,000,000
At each annual settlement date:
Party A Party B$500,000
10,400,000At maturity:
Party A Party B$10,000,000
1,040,000,000
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Cash Flows in a Fixed-for-FloatingCurrency Swap
On the origination date: The fixed rate payer pays $10,000,000 to the fixed rate receiver.
The fixed rate receiver pays 1,040,000,000 to the fixed rate payer.
Fixed rate payer(Floating rateReceiver)
Fixed rate Receiver
(Floating RatePayer)
$10,000,000
1,040,000,000
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Calculating Subsequent Cash Flowsfor this Fixed-for-Floating Currency
Swap
Tenor is three years. NP1 = 1,040,000,000 yen, and r1 =1% fixed in yen. NP2 = $10,000,000, and r2 = 6 month $-
LIBOR (floating). Settlement dates are every 6 months,beginning 6 months hence.
On the origination date, 6 month LIBOR is 5.5%.
Assume that subsequently, 6 mo. LIBOR is:
Time 6 mo. LIBOR0.5 5.25%
1.0 5.50%
1.5 6.00%
2.0 6.20%
2.5 6.44%
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All Cash Flows for this Fixed-for-Floating Currency Swap
6-mo. Fixed rate Floating ratetime LIBOR Payment Payment
0.0 5.50% $10MM 1,040MM0.5 5.25% 5.2MM $275,000
1.0 5.50% 5.2MM $262,50011.5 6.00% 5.2MM $275,0002.0 6.20% 5.2MM $300,0002.5 6.44% 5.2MM $310,0003.0 ---- 5.2MM $322,000
1,040MM $10MM
N.B. The time t floating cash flow is determined using the time t-1floating rate.
1 Time 1.0 floating rate payment is (0.0525/2)($10,000,000) =
$262,500.
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Credit Risk: Currency Swaps
Note that there is greater credit risk with acurrency swap when there will be a final
exchange of principal.
This means that there is a higher probability ofa large buildup in value, giving one of thecounter-parties (the one who is losing) theincentive to default.
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Credit Risk
No credit risk exists when a swap is first created. The credit risk in a swap is greater when there is
an exchange of principal amounts at termination. Only the winning party (for whom the swap is an
asset) faces credit risk. This risk is the risk thatthe counter-party will default.
Many vehicles exist to manage credit risk: Collateral (or collateral triggers)
Netting agreements Credit derivatives Marking to market
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Other Currency Swap Structures
See the different interest rate swap structurespresented earlier. They all apply to currencyswaps, too.
Index differential swaps, or diff swaps: The cash flows are based on two floating rates in
different countries, but they are applied to the NPofone of the currencies.
For example, pay-based LIBOR, and receive $-based LIBOR, on a NP of $20MM. All paymentsare in $.
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Commodity Swaps
Equivalent to a strip of forward contracts on acommodity.
Define NP in terms of the commodity; e.g., 10,000
oz. of gold. The NP is not exchanged.
Define Pfixed as the fixed price.
Payments are made by comparing the actual price of
the commodity on the settlement date (or an averageprice over the period, or the actual price one periodearlier) to the fixed price.
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Commodity Swaps: an Example, I.
A gold mining firm wants to fix the price it will receive forthe gold it will mine over the next 3 years.
A gold user wants to fix the price it will have to pay forthe gold it needs for the next 3 years.
NP = 10,000 oz.
Pfixed = $320/oz.
Settlement is semi-annual, based on average price ofgold during the past six months.
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Commodity Swaps: an Example, II.
Subsequently:
Avg. gold price Producerpays(-)
Time during past pd. orreceives(+)0.5 $305 +$150,000
1.0 $330 -$100,000
1.5 $368 -$480,000
2.0 $402 -$820,000
2.5 $348 -$280,0003.0 $300 +$200,000